View Single Post
Old 2004-04-27, 13:46   #18
R.D. Silverman
 
R.D. Silverman's Avatar
 
Nov 2003

22·5·373 Posts
Thumbs up

Quote:
Originally Posted by jinydu
For example, simplify the following:

cbrt(-54+sqrt(2700))+cbrt(-54-sqrt(2700))

This time, I will not give out the answer a priori (although this particular case was also handpicked carefully). Also, the technique (maybe algorithm is an even better word) you use should also work for:

cbrt(10 + sqrt(108)) + cbrt(10 - sqrt(108))

I get cbr(-6). Once again if there is a simplified form it must lie
within the maximal order of one of the subfields of Q(alpha) [assuming
a monic polynomial]. Find a basis for the subfield. This gives an expression
for each element within its maximal order. Equate this expression to
your original number and solve for the coefficients.
R.D. Silverman is offline   Reply With Quote